Abstract:
The game of Set is a simple but addictive card game played with a special 81-card deck; it is the also the most mathematically rich popular entertainment since Rubik's Cube. A standard "folklore question" among players of this game is: what is the largest number of cards that can be on the table which do not allow a legal play? I'll explain some of the strategies a mathematician would use to approach the Set problem; the key idea is an analogy between the deck of cards and 4-dimensional space, which turns the question into a geometry problem! In fact, the Set problem turns out to be part of one of the most energetically pursued problems in combinatorics, the "affine cap problem," which is very simple to state and about which we know embarrassingly little—though a paper released last year by Bateman and Katz provides the first new progress in many years. If there's time, I'll try to convince you that the Set problem might have something to do with algebraic geometry, and in the unlikely event there's even more time, I'll try to convince you that, no, in fact, it really has to do with Fourier analysis.

Speaker biography: Jordan Ellenberg is a professor at the University of Wisconsin-Madison, specializing in number theory and arithmetic geometry. Before starting his Ph.D. he wrote a novel, The Grasshopper King, which was published in 2003. Ellenberg did his graduate work at Harvard, where he had the pleasure of seeing Serge Lang lecture several times. He also writes about math in general-interest publications, including Slate, Wired, the New York Times Magazine, and the Believer, and was a script consultant for season 2 of the CBS math-cop drama Numb3rs. He blogs about mathematics, baseball, food, and culture at Quomodocumque.

The origin of this lecture was a particularly bad beating at Set Ellenberg received from an 8-year-old boy, after which he became determined to understand something about the game that a small child could not.